sustainability

Article Numerical Simulation and Design of Multi-Tower Concentrated Fields

Zaharaddeen Ali Hussaini 1,2,*, Peter King 1 and Chris Sansom 1 1 School of Water and Environment, Cranfield University, Cranfield MK43 0AL, UK; peter.king@cranfield.ac.uk (P.K.); c.l.sansom@cranfield.ac.uk (C.S.) 2 Centre for Research, Bayero University, Kano 700241, Nigeria * Correspondence: zaharaddeen-ali.hussaini@cranfield.ac.uk or [email protected]

 Received: 7 February 2020; Accepted: 10 March 2020; Published: 19 March 2020 

Abstract: In power tower systems, the field is one of the essential subsystems in the plant due to its significant contribution to the plant’s overall power losses and total plant investment cost. The design and optimization of the heliostat field is hence an active area of research, with new field improvement processes and configurations being actively investigated. In this paper, a different configuration of a multi-tower field is explored. This involves adding an auxiliary tower to the field of a conventional power tower (CSP) system. The choice of the position of the auxiliary tower was based on the region in the field which has the least effective reflecting . The multi-tower configuration was initially applied to a 50 MWth conventional field in the case study region of Nigeria. The results from an optimized field show a marked increase in the annual output and mean annual efficiency of the field. The biggest improvement in the optical efficiency loss factors be seen from the cosine, which records an improvement of 6.63%. Due to the size of the field, a minimal increment of 3020 MWht in the Levelized Cost of Heat (LCOH) was, however, recorded. In much larger fields, though, a higher number of weaker heliostats were witnessed in the field. The auxiliary tower in the field provides an alternate aim point for the weaker heliostat, thereby considerably cutting down on some optical losses, which in turn gives rise to higher energy output. At 400 MWth, the multi-tower field configuration provides a lower LCOH than the single conventional power tower field.

Keywords: concentrated solar power; field layout; heliostat field; multi-tower field

1. Introduction Due to the declining patronage of nuclear energy and volatile petroleum and natural gas prices, coupled with the rising global temperature, predominately due to the atmospheric build-up of CO2, nations at large are opting for and considering renewable energy technologies for their power generation. , in particular, is seen as an extremely viable option, especially in areas with good solar insolation [1]. for generation is typically referred to as Concentrated Solar Power (CSP) [2]. CSP can be a driving force in the cause of reducing CO2 emission, thereby contributing to reducing and limiting the global temperature increase. Of the existing types of CSP, power tower systems are one of the most promising solar thermal technologies. This is mainly due to their ability to offer higher temperatures and, hence, higher efficiencies [2–7]. In power tower systems, the heliostat field is one of the essential subsystems. This is due to its significant contribution to the plant’s total investment cost: about 40%–50% of the plant’s cost is attributed to the heliostat field [8–12]. The field contributes equally to the plant’s overall power losses of about 40% [8,13–16]. It has hence become essential to ensure that the field layout is optimal at collecting energy from the sun. The design and optimization of the heliostat field is hence an

Sustainability 2020, 12, 2402; doi:10.3390/su12062402 www.mdpi.com/journal/sustainability Sustainability 2020, 12, 2402 2 of 22 active area of research, with new field improvement processes being actively investigated. Several methods have been proposed in the literature to improve heliostat field efficiencies and reduce losses, either by improving through optimization or by suggesting new heliostat field layout patterns and configurations entirely. Several literatures that focus on heliostat field layout patterns and configurations are available. In Noone et al.’s [8] , for example, a spiral field pattern inspired by disc phyllotaxis is introduced, which is applied in heliostat field design and optimization. By redesigning the layout of the PS10 field using the algorithm, an improvement in the optical efficiency and a reduction in the land area utilized is witnessed. E. Carrizosa et al. [17] presented a pattern-free heliostat field layout distribution style, obtained by the simultaneous optimization of both the heliostat field (heliostat locations and number) and the tower (tower height and receiver size). Cadiz et al. [10] presented shadowing and blocking optimization procedures for a variable-geometry heliostat field. The variable-geometry concept explored by the author allows the possibility of minimizing the cosine losses by rotating the entire field. In a similar vein, Mohammed Aldulaimi and MS Soylemez [14] suggested a new heliostat field layout arrangement by identifying heliostats with low optical efficiency and increasing their heights in a bid to curb blocking losses and hence increase the total annual field efficiency. Emilo Carrizosa [18] also suggested some alterations in the field by considering a field with different heliostat sizes. Mani Yousefpour Lazardjan [19] presented a tool developed at Solar-Insitut Julich (SIJ) primarily for the optimization of a novel micro-heliostat concept. In a novel and unconventional heliostat field layout design, Danielli et al. [20] developed the concatenated micro-tower (CMT). In this configuration, dynamic receivers mounted on arrays of small towers enable heliostats in mini subfields to direct sunlight with minimal cosine losses, thus improving the field’s overall optical efficiency. N. Cruz et al. [21] also developed an algorithm using a genetic algorithm that generates a continuous pattern-free field layout. The algorithm developed, using parallelization, provides a solution to the conceptual complexity and high computational cost associated with pattern-free heliostat field optimization. Arrif et al. [22] also developed an algorithm which is based on the bee colony optimization method to optimize the case study site of the PS10 CSP power plant in Spain. The proposed algorithm, the Artificial Bee Colony Algorithm (IABCA), finds the best position for each heliostat on the field in which the maximum efficiency for both the heliostat and field is reached within a limited area. L Deng et al. [23] proposed a new pattern for the heliostat field layout: a rose pattern based on the classic radial staggered configuration. The pattern divides the radial staggered configuration into six sectors, and some of those sectors are then optimized separately using advanced differential equation algorithm, thus increasing the optimization variables. In another unconventional heliostat field layout design, additional towers, each having its receiver mounted atop, are introduced in the field. Although it is only recently that the multi-tower setup has attracted much interest in the research community, the configuration has been explored in the past. In 1999, Romero et al. [24] pointed out that centralized large plants are at odds with the increasing shift towards a distributed-energy setup and could hence face future deployment difficulties. They proposed and analyzed how small tower fields could be integrated into a Modular Integrated Utility Systems (MIUS) approach, in order to fully exploit the advantages of a distributed-energy setup in a community. In 2002, Schramek and Mills [25] proposed a Multi-Tower Solar Array (MTSA) system, which consists of a collection of solar towers densely grouped together, thereby allowing for partial overlapping of the heliostats in the field, and hence allowing greater utilization of the solar radiation falling on the unused ground area in the field. In a more recent work, in 2012, Augsburger and Favrat [26] proposed a method in which each individual heliostat is instantaneously aimed at a receiver in a multi-tower setup, following an aim selection criterion. The thermo-economic performance of a three-tower heliostat field was then evaluated using a model. In another work, eSolar and Inc. (B&W PGG) [27] investigated the use of small heliostats with multiple receivers and towers [27]. They proposed a configuration with 14 molten salt power towers, for a 100 MWe (net) power block that is capable of delivering a Sustainability 2020, 12, 2402 3 of 22

75%Sustainability capacity factor.2017, 9, x Tyner FOR PEER and REVIEW Wasyluk [28] presented a follow-through on the conceptual design3 of 22 previously developed by eSolar and Inc., where several trade studies were carried out in order to arrive carried out in order to arrive at the optimally cost-effective system configuration for the multi-tower at the optimally cost-effective system configuration for the multi-tower setup. The concept proposed setup. The concept proposed involves replicating the field, without scaling or redesign, in order to involves replicating the field, without scaling or redesign, in order to meet the capacity required. meet the capacity required. In another work by Pasha Piroozmand and Mehrdad [29], an iterative In another work by Pasha Piroozmand and Mehrdad [29], an iterative algorithm was developed in algorithm was developed in order to obtain the optimum instantaneous efficiency of the heliostat in order to obtain the optimum instantaneous efficiency of the heliostat in the field when selecting the the field when selecting the tower which radiation will be reflected onto in a two-tower field set up, tower which radiation will be reflected onto in a two-tower field set up, so as to maximize the annual so as to maximize the annual optical efficiency of the field. As a case study, the authors used Particle optical efficiency of the field. As a case study, the authors used Particle Swarm Optimization (PSO) to Swarm Optimization (PSO) to optimally design a two-tower spiral patterned field along the east-west optimally design a two-tower spiral patterned field along the east-west line before redesigning the line before redesigning the field using the iterative method. The authors here noted that issues such field using the iterative method. The authors here noted that issues such as field layouts and aiming as field layouts and aiming strategies need to be further investigated in order to achieve a more strategies need to be further investigated in order to achieve a more optimized and comprehensive optimized and comprehensive multi-tower system. In 2018, Vast Solar, an Australian company multi-tower system. In 2018, Vast Solar, an Australian company engaged in CSP research, developed engaged in CSP research, developed and commissioned a 1.1MWe pilot plant utilizing a modular and commissioned a 1.1MWe pilot plant utilizing a modular solar array field [30]. Each of the five solar array field [30]. Each of the five modular arrays in the field has a dedicated tower in which the modular arrays in the field has a dedicated tower in which the Heat Transfer Fluid (HTF) is heated Heat Transfer Fluid (HTF) is heated at the receiver. The multiple towers are connected to a central at the receiver. The multiple towers are connected to a central thermal storage unit. The company is thermal storage unit. The company is already planning to go further by developing a 30MW already planning to go further by developing a 30MW commercial demonstration project in Australia commercial demonstration project in Australia using the modular array field. using the modular array field. In all the multi-tower configurations reviewed, each tower has its own heliostat field, which In all the multi-tower configurations reviewed, each tower has its own heliostat field, which replaces an entire field with surrounding heliostats in smaller units until the capacity required is met. replaces an entire field with surrounding heliostats in smaller units until the capacity required is met. In this paper, a different architecture of the multi-tower configuration is investigated. The In this paper, a different architecture of the multi-tower configuration is investigated. The configuration configuration explored, which provides an alternate viewpoint to the usual mainstream multi-tower explored, which provides an alternate viewpoint to the usual mainstream multi-tower configuration, configuration, involves adding an auxiliary tower to an existing surrounding field. The paper initially involves adding an auxiliary tower to an existing surrounding field. The paper initially begins by begins by defining the models used for the development of a conventional heliostat field. After model defining the models used for the development of a conventional heliostat field. After model validation, validation, a 50MWth solar field was simulated in Nigeria, with the objective function being the a 50 MWth solar field was simulated in Nigeria, with the objective function being the Levelized Cost of Levelized Cost of Heat (LCOH). An auxiliary tower was then added onto the existing field, and its Heat (LCOH). An auxiliary tower was then added onto the existing field, and its effects investigated. effects investigated. The results from the optimized multi-tower configuration were then compared The results from the optimized multi-tower configuration were then compared with conventional with conventional fields at different thermal field powers, in order to determine the optimum fields at different thermal field powers, in order to determine the optimum transition size from a single transition size from a single field to a multi-tower field. field to a multi-tower field.

2. Model2. Model Description Description

2.1.2.1. Solar Solar Insolation, Insolation, Time Time and and Angles FindingFinding the the position position of the of the sun sun is one is one of the of the very very first first steps steps that that needs needs to be to taken.be taken. The The position position cancan be characterizedbe characterized by the by altitudethe altitude (α) and (α) azimuthand azimuth angle (γs). Figure (γs). Figure1 shows 1 shows the angles the definingangles defining the apparentthe apparent position position of the sun of the [12 ,sun31]. [12,31],

Figure 1. Position of the sun relative to the collector. Figure 1. Position of the sun relative to the collector.

where is the zenith angle and Sx, Sy, and Sz denote the vector components of the sun’s radiation. The solar altitude is given by Equation 1 [31]: Sustainability 2020, 12, 2402 4 of 22

→ Where θz is the zenith angle and Sx, Sy, and Sz denote the vector components S of the sun’s radiation. The solar altitude is given by Equation (1) [31]:

Sinα = SinϕSinδ + CosϕCosδCosω (1) where latitude, ϕ, is angular location relative to the equator, and declination angle, δ, is the angular position of the sun at solar noon on the equatorial plane. The declination angle is given by Equation (2):

 284 + n δ = 23.45Sin 360 (2) × 365 where n represents the day number of the year [31], and ω is the Hour angle (east or west angular displacement of the sun about the local meridian due to earth’s rotation about its polar axis). It is represented in Equation (3), with t being the solar time [31].

ω = 15 (t 12) (3) × − The azimuth angle, on the other hand, is given by Equation (4) [31]

CosδSinω Sinγ = (4) s Cosα Specific geographical locations in Nigeria are highly suitable for the deployment of solar energy technologies, especially in the northern parts of the country. For regions in the northern parts of Nigeria, a Direct Normal Irradiance (DNI) average value of around 5.5 kWh/m2/day is obtainable [32–34], making the area suitable for CSP deployment. The solar insolation at the selected site, Katsina, Nigeria (Latitude: 12.39◦ N Longitude: 7.60◦ E), was obtained from the metrological agency in Nigeria, NiMet (Nigerian Metrological Agency). The DNI at the identified site averages out to 5.53 kWh/m2/day.

2.2. Optical Efficiency The optical efficiency of the field measures the capability of each heliostat to concentrate and reflect radiation to the receiver. Every heliostat has a particular optical efficiency value due to its position in the field and its interaction with the other elements in the field. The overall value for the field is then calculated by averaging each particular result. The optical field efficiency is expressed by Equation (5) [8,12,35]; η = η η η η η (5) f ield cos × sb × att × int × re f where ηcos, ηsb, ηatt, ηint, and ηre f represent losses due to cosine, shadowing and blocking, atmospheric attenuation, interception and mirror reflectivity factors, respectively. Maximizing field efficiency is an important task that ensures the optical losses are reduced as much as possible.

2.2.1. Cosine Efficiency Loss The cosine efficiency loss is one of the most critical energy loss sources in heliostat fields and often represents the most significant loss term [36]. It is defined as the cosine of the angle formed by the incident solar beam radiation and the vector normal to the reflective heliostat surface [37]. The efficiency factor depends on both the position of the sun and of the heliostat [12]. Figure2 shows the effect of cosine on reflected rays from the heliostat. To evaluate the normal vector of the heliostat surface, two other vectors need to be defined, i.e., the vectors from the center of the heliostat to the sun, →S, and those to the desired image location on Sustainability 2020, 12, 2402 5 of 22

the receiver surface, →r . Assuming x, y, and z are the coordinates of the heliostat center, and TH is the tower height, the components of the unit vector of the reflected ray, →r is given by Equation (6) [38,39]:      x y (TH z)  →   r =  q − , q − , q −  (6)  2 2 2   x2 + y2 + (TH z) x2 + y2 + (TH z) x2 + y2 + (TH z)  Sustainability 2017, 9, x FOR PEER REVIEW − − − 5 of 22

Figure 2. Figure showing the effect of cosine on reflected rays in Heliostat A and B. Figure 2. Figure showing the effect of cosine on reflected rays in Heliostat A and B. Vector →S components are formed from Figure1. With →S and →r defined, the components of the unit vector normal of the heliostat surface can then be evaluated (Equation (7)): To evaluate the normal vector of the heliostat surface, two other vectors need to be defined, i.e., the vectors from the center of the heliostat to the →sun,S + →r , and those to the desired image location on m→ = (7) the receiver surface, . Assuming x, y, and z are the →S + coordinate→r s of the heliostat center, and TH is the tower height, the components of the unit vector of the reflected ray, is given by Equation 6 [38,39]:

The cosine efficiency− can now be calculated as the− dot product of the unitary( vectors − ) m→ and →S, as shown in = Equation (8): , , (6) + +(−) + +(−) + +(−) η = m→ →S (8) cos · Vector components are formed from Figure 1. With and defined, the components of the 2.2.2. Shadowing and Blocking Efficiency Loss unit vector normal of the heliostat surface can then be evaluated (Equation 7): Shadowing and blocking losses are a result of the reduction of the heliostat’s useful area due to the presence of a heliostat in the path of the incident radiation+ or to reflected radiation, respectively. = (7) In Figure3, the contour of the representative heliostat + and the projected contour of the two adjacent heliostats in a radial staggered configuration is shown. The cosineHere, efficiency bh and bw can are the now blocking be calculated and shadowing as the portions dot product of the representative of the unitary heliostat. vectors LH and and , as shownLW in are Equation the heliostat’s 8: length and width, respectively. DM is the diameter of the heliostat, inclusive of dsep (the extra security distance between adjacent heliostats).

The blocking and shadowing model adopted = the ⋅ simplified calculation method developed by (8) Sassi [40], using the outline projections of the neighboring heliostats. This method divides the surfaces of each heliostat into strips, and those strips identified to have potential for shadowing and blocking 2.2.2. Shadowingare projected and onto Blocking the surface Efficiency of the problem Loss heliostat. Among all the shading and blocking projections, the maximum height is selected for each strip. The fraction of the area free from shading and blocking Shadowinggives the shadingand blocking and blocking losses effi areciency a result value. of the reduction of the heliostat’s useful area due to the presenceAs of toa heliostat the identification in the path and selection of the incide of thent shadowing radiation and or blockingto reflected heliostats, radiation, the method respectively. In Figureoutlined 3, the contour in [37] by of Besarati the representative and Goswami is helio adopted.stat Thisand methodology the projected considers contour only of a the subset two of adjacent heliostatsthe in heliostats a radial that staggered have a high configuration potential for shadowingis shown. and blocking. For shading, a circle of radius

Figure 3. Blocking showing the contour of the representative heliostat and the projected contour of two adjacent heliostats in the first-row. Sustainability 2017, 9, x FOR PEER REVIEW 5 of 22

Figure 2. Figure showing the effect of cosine on reflected rays in Heliostat A and B.

To evaluate the normal vector of the heliostat surface, two other vectors need to be defined, i.e., the vectors from the center of the heliostat to the sun, , and those to the desired image location on the receiver surface, . Assuming x, y, and z are the coordinates of the heliostat center, and TH is the tower height, the components of the unit vector of the reflected ray, is given by Equation 6 [38,39]: − − ( − ) = , , (6) + +(−) + +(−) + +(−)

Vector components are formed from Figure 1. With and defined, the components of the unit vector normal of the heliostat surface can then be evaluated (Equation 7): + = (7) +

The cosine efficiency can now be calculated as the dot product of the unitary vectors and , as shown in Equation 8:

= ⋅ (8)

Sustainability2.2.2. Shadowing2020, 12, 2402and Blocking Efficiency Loss 6 of 22 Shadowing and blocking losses are a result of the reduction of the heliostat’s useful area due to Rthesb = presence2.5DM isof initiallya heliostat drawn in the around path of the the centre incide ofnt the radiation analyzed or heliostat. to reflected The radiation, vector connecting respectively. the centreIn Figure of the 3, analyzedthe contour heliostat of the isrepresentative then projected helio to thestat sun and on the the projected horizontal contour plane. of The the heliostats two adjacent near theheliostats projection in a areradial identified staggered to have configuration the highest is potentialshown. to shade and thus selected for the analysis.

Figure 3. Blocking showing the contour of the representative heliostat and the projected contour of twoFigure adjacent 3. Blocking heliostats showing in the the first-row. contour of the representative heliostat and the projected contour of two adjacent heliostats in the first-row. With the radial staggered configuration (the adopted field layout generation methodology), the method from Besarati and Goswami is not required for the identification of the blocking heliostats, as this can quickly be done by considering the ‘shoulder’ heliostats at the next row (Figure3) of the analyzed heliostat and the one that is two rows over and directly in front of it [41].

2.2.3. Attenuation Efficiency Loss The radiation reflected from the heliostat does not wholly reach the receiver. This is because some energy is scattered and/or absorbed by the atmosphere. Atmospheric attenuation consists of energy losses in the reflected radiation during passage through the atmosphere from each heliostat to the receiver. This is an efficiency factor that is typically dependent on the distance of the heliostat relative to the tower, the aerosol distribution at the ground level, and site altitude [42]. On a day when visibility is good, the energy loss will be a small percentage of the energy loss per kilometer. This atmospheric attenuation efficiency can be calculated using Equation (9), as provided in [43], for fields with a distance between heliostat and receiver aim point below 1000 m:

8 2 η = 0.99321 0.0001176D + 1.97 10− D D 1000m (9) att − × × ≤ The formula in Equation (9) was extended by M.Schmitz et al. [44] For larger fields, see Equation (10): η = exp( 0.0001106D) D > 1000m (10) att − where D is the distance between the heliostat and the aim point of the receiver.

2.2.4. Interception Efficiency Loss The interception efficiency loss, otherwise known as spillage, refers to reflected energy directed towards the receiver that does not fall on the absorbing area. The factor is dependent on both the heliostats in the field and the receiver design and properties [12]. While the ‘spill’ of the reflected radiation can be reduced by increasing the receiver size, consideration of other receiver energy losses and receiver costs must be made. A description of the spilled radiation is shown in Figure4. The spillage can be calculated by integrating the image shape produced by the mirror over the receiver domain [44–48]. Sustainability 2020, 12, 2402 7 of 22 Sustainability 2017, 9, x FOR PEER REVIEW 7 of 22

Figure 4. A demonstration of spillage on the receiver. Figure 4. A demonstration of spillage on the receiver. The University of Zaragoza (UNIZAR) [46] and HFLCAL [48] methods are widely used for the analyticalThe expressionsUniversity of of Zaragoza interception (UNIZAR) efficiency [46] and and appropriate HFLCAL [48] tools methods for design are widely and optimization. used for the Theanalytical HFLCAL expressions model, from of theinterception German Aerospace efficiency Centreand appropriate (DLR), is applied tools for in design this paper. and Theoptimization model is . adjudgedThe HFLCAL to be bothmodel, simpler from andthe German slightly moreAerospace accurate Centre that (DLR), the UNIZAR is applied method in this [47 paper.]. The HFLCALThe model model’sis adjudged flux density to be expressionboth simpler is aand circular slightly normal more distribution. accurate that The the effi ciencyUNIZAR loss method is expressed [47]. byThe EquationHFLCAL (11) model’s [44,48 ];flux density expression is a circular normal distribution. The efficiency loss is expressed by Equation 11 [44,48]; Z Z ! 1 · · x2 + y2 η = . . − (11) int 2 exp 2 dydx 2πσ1tot 2σ tot+ = x0 y0 − (11) 2 2 where x0 and y0 are coordinates of the plane normal to the receiver surface and σtot is the standard deviationwhere x’ of and the y’ flux are distribution coordinates on of thethe receiverplane normal plane to given the byreceiver Equation surface (12) and [44]; is the standard deviation of the flux distribution on the receiver plane given by Equation 12 [44]; q 2 2 2 2 2 σtot = D (σ tot + σ + σ ast + σ tr) (12) bq = ( + + + ) (12) where σsun, σbq, σast, σtr are the standard deviations due to sun shape error, mirror slope error, astigmatic error,where and tracking, , error,, respectively. are the standard A sun shape deviations error value due of to 2.51 sun mrad, shape as measurederror, mirror in Planta slope Solarerror, Almeriaastigmatic (PSA) error, [41 ],and is appliedtracking here. error, The respectively. beam quality A sun value shape is assumed error value to be of 1.882.51 mrad,mrad, asas reportedmeasured in Planta Solar Almeria (PSA) [41], is applied here. The beam quality value is assumed to be 1.88 in [49]. Also, as in [49], the σtr is assumed at 0.63, a value obtained from tests on the SENER heliostat mrad, as reported in [49]. Also, as in [49], the is assumed at 0.63, a value obtained from tests on under low wind conditions. The astigmatism effect σast, can be calculated by Equation (13) [44]; the SENER heliostat under low wind conditions. The astigmatism effect , can be calculated by q Equation 13 [44]; ( 2 + 2) 0.5 Ht Ws σast = (13) 0.5 4(D + ) = (13) 4 where Ht and Ws are the image dimensions in the tangential and sagittal planes at the receiver position. Thewhere values areand given are by Equationthe image (14) dimensions [44]; in the tangential and sagittal planes at the receiver position. The values are given by Equation 14 [44];

D D H = √LW + LH Cosε , W = √LW + LH Cos ε 1 (14) t = √ + −Cos , s = √ + Cos − 1 (14) f − f − wherewhere f isf is the the focal focal distance distance of of the the heliostat heliostat surface surface andandCos ε is is the the incidence incidence cosine cosine between between the the sunrayssunrays and and the the heliostat heliostat normal. normal.

2.2.5.2.2.5. Mirror Mirror Reflectivity Reflectivity Loss Loss MirrorMirror reflectivity reflectivity a ffaffectsects the the amount amount of of radiation radiation that that can can be be redirected redirected by by the the heliostat. heliostat. This This is is primarilyprimarily due due to to the the design design specifications specifications and and condition condition of of the the heliostat. heliostat. A A uniform uniform reflectivity reflectivity value value ofof 0.88 0.88 is is adopted adopted here, here, as as in in [8 [8,49].,49]. The The reflectivity reflectivity effi efficiencyciency can can hence hence be be fully fully expressed expressed as: as:

η ==0.88 0.88 ( ×0.95 (0.95)) (15)(15) re f × where the 0.95 factor is the nominal value adopted for cleanliness. In this work, the is assumed constant for all heliostats in the field.

2.3. Field Layout Model Sustainability 2020, 12, 2402 8 of 22

where the 0.95 factor is the nominal value adopted for cleanliness. In this work, the ηre f is assumed constant for all heliostats in the field. Sustainability 2017, 9, x FOR PEER REVIEW 8 of 22 2.3.Sustainability Field Layout 2017 Model, 9, x FOR PEER REVIEW 8 of 22 In this paper, the proposed method for the field layout and generation is the radial staggered distribution.InIn this this paper, paper,The theconfiguration the proposed proposed method providesmethod for fora the thewell field fiel-establishedd layout layout and and and generation generation tested ismethodology is the the radial radial staggered staggeredfor the distribution.generationdistribution. of The a Theheliostat configuration configuration field. providesThe radialprovides a well-establishedstaggere a welld arrangement-established and tested ensuresand methodology tested that nomethodology heliostat for the generation is placedfor the ofdirectlygeneration a heliostat in front of field. aof heliostat another The radial heliostatfield. staggered The in radial adjacent arrangement staggere rings.d In arrangement ensures this way, that a reflectedensures no heliostat thatbeam isno from placed heliostat any directly heliostat is placed in frontpassesdirectly of between another in front heliostatits of adjacentanother in heliostatadjacentneighbors in rings. adjacenton the In thisway rings. way, to In the athis reflected receiver way, a beam reflected[50]. fromFigure beam any 5 fromshows heliostat any a typicalheliostat passes betweenrepresentationpasses itsbetween adjacent of theits neighbors radialadjacent staggered onneighbors the way configuration toon thethe receiver way [38]. to [ 50the]. Figurereceiver5 shows [50]. Figure a typical 5 representationshows a typical ofrepresentation the radial staggered of the configurationradial staggered [38 ].configuration [38].

. . Figure 5. Radial staggered configuration. Figure 5. Radial staggered configuration. Figure 5. Radial staggered configuration. The method for the generation of the radial staggeredstaggered layout presented inin [[13]13] (campo) is applied here. OneThe of method the purposes for the ofgeneration this code, of developed the radial bystagge FJ Collado, red layout is to presented improve in the [13] accuracy (campo) and is applied speed withwithhere. whichwhich One theofthe the heliostatheliostat purposes fieldfield of isthisis optimizedoptimized code, developed andand designed.desi bygned. FJ Collado, This makes is to improve it convenientconvenient the accuracy forfor thethe intendedintended and speed applicationwith which here.here. the Detailsheliostat of field the campois optimized steps are and outlinedoutlined designed. inin [[13,51].This13,51 makes]. it convenient for the intended applicationThe fieldfield here. isis initiallyinitially Details laidlaid of the outout campo byby developingdeveloping steps are outlined the densest in [13,51]. fieldfield made up ofof concentricconcentric rows of heliostats.The Thefield field field is initially is gradually laid expandedout by developing by altering the the densest radial separationfield made distances, up of concentric ∆ΔR, during rows the of optimizationheliostats. The process.process. field is The gradually parameters expanded in the layoutby altering of the the fieldfield radial areare separation shownshown inin Figure Figuredistances,6 6:. ΔR, during the optimization process. The parameters in the layout of the field are shown in Figure 6:

FigureFigure 1. 6. ParametersParameters definingdefining thethe layoutlayout ofof thethe field.field. Figure 1. Parameters defining the layout of the field. The densest field has Δ, with the minimum radial increase at: The densest field has Δ, with the minimum radial increase at: Δ = 30⁰ (16) Δ = 30⁰ (16) where DM is the horizontal clearance, , added to the heliostat diagonal length (DH). where DM is the horizontal clearance, , added to the heliostat diagonal length (DH). Sustainability 2020, 12, 2402 9 of 22

The densest field has ∆Rmin, with the minimum radial increase at:

∆Rmin = DM Cos30 ◦ (16) where DM is the horizontal clearance, dsep, added to the heliostat diagonal length (DH).

DM = DH + dsep (17)

The heliostat field layout procedure for generating the heliostat configuration begins by placing the first heliostat tangential to the Y-axis (North) at radius distance R1 from the center, where the tower is situated. The second heliostat is placed at the same radius distance, at an azimuth angle distance, ∆az1, from the initially placed heliostat. This placement continues through the entire row. This process is continued on subsequent rows of the field, with the first row being odd and the second row even (starting point here is at the Y-axis), in order to provide the needed staggered configuration. The azimuthal distance ∆az1, can be expressed by Equation (18):   1 DM ∆az = 2Sin− (18) 1 2R1 R1 can be determined by the following:

DM R1 = Nhel (19) 1 2π where Nhel1 is the number of heliostats in the first row. As the consecutive rows are increased, the distance between the heliostats widens until it eventually becomes higher than DM. At his point, a new zone is created in which layout generation is started afresh. The number of zones in this developed model is limited to three. In the new zone, the radius from the tower can be calculated by; ! i 1 DM Ri = 2 − (20) ∆az1 where i signifies the subsequent zones in the field. The angular spacing in the ith zone in the field can also be determined by:  ∆az  ∆az = 1 (21) i i 1 2 − With the field layout generated, expansion and optimization of the field can then be initiated. In this particular model, the optimization is not only limited to improving the optical efficiency but also obtaining the parameters of the field. The parameters of the field constitute the design variables (namely, the number of heliostats in the first row, heliostat area, tower height, and consecutive row separation distance in the first, second, and third zones). The design variables are optimized using a Genetic Algorithm (GA) within the context of the chosen objective function to arrive at the required field thermal power. The model is developed using the computer programming language MATLAB developed by MathWorks.

Model Validation Table1 compares the results presented in the reference model, campo, by F.J Collado [ 49] to those of the one developed here. The campo model uses data and references from the Gemasolar plant in Sevilla, the first commercial plant with molten salt storage. The field data and specifications used for model validation in the Gemasolar plant are outlined in [49]. Sustainability 2020, 12, 2402 10 of 22

Table 1. Model results in comparison to campo method.

Zone 1 Zone 2 Zone 3 Zones Field Efficiency Ref Model Model Diff Ref Model Model Diff Ref Model Model Diff Row Spacing (m) (%) (%) (%) (%) (%) (%) (%) (%) (%) ∆R1 = 0.866DM ∆R2 = 0.866DM 65.34 65.21 0.20 55.42 55.12 0.54 37.54 37.34 0.53 ∆R3 = 0.866DM ∆R1 = 0.866DM 65.36 65.21 0.23 58.45 58.59 0.24 48.05 47.79 0.54 ∆R2 = 1.4DM − ∆R3 = 1.4DM ∆R1 = 0.866DM 65.36 65.21 0.23 57.85 57.86 0.02 48.35 48.27 0.17 ∆R2 = 1.6DM − ∆R3 = 1.6DM ∆R1 = 0.866DM ∆R2 = 1.4DM 65.36 65.21 0.23 58.66 58.79 0.22 50.26 49.98 0.56 − ∆R3 = 1.6DM ∆R1 = 0.866DM 65.36 65.21 0.23 58.77 58.89 0.20 51 50.78 0.43 ∆R2 = 1.4DM − ∆R3 = 1.8DM ∆R1 = 0.866DM 65.36 65.21 0.23 58.75 58.89 0.24 51.07 50.69 0.74 ∆R2 = 1.4DM − ∆R3 = 2.0DM ∆R1 = 0.866DM 65.36 65.21 0.23 58.68 58.89 0.36 50.9 50.58 0.63 ∆R2 = 1.4DM − ∆R3 = 2.2DM

The results in Table1 show that all the field e fficiency values are within a 1% margin difference. The differences can be attributed to the solar radiation data used. Although the data is from the same location in Seville, Spain, the reference model uses Typical Meteorological Year (TMY) data. The model developed, due to unavailability of data, utilizes measured data for a limited period (the years 2013–2014). The difference may also be a result of the optical loss model for shadowing and blocking utilized, which differs from the one used in the reference model.

3. Design and Optimization

3.1. Conventional Field The validated model was then applied to the selected site in order to design and optimize, initially for the conventional field, a 50 MWth field. As earlier stated, the field in power tower systems has a significant weighting effect on the overall plant efficiency. This, in addition to being the most expensive part of the plant, further necessitates the importance of optimization in designing the heliostat field layout. In this work, the primary objective function considered in optimization was in the form of minimizing a simplified Levelized Cost of Heat given by Equation (22) [52–54]. In calculating LCOH, only an independent generating system was assumed:

Total Heliostat Field Li f e Time Cost Total Li f e Time Output o f Annual Thermal Energy Generated at Receiver Sur f ace Field Installed Cost CRF (22) = ∗ + O&M Eth where O&M signifies the operating and maintenance cost, and CRF is the uniform series capital recovery factor. The CRF is given by Sustainability 2020, 12, 2402 11 of 22

ir(1 + i)N CRF = (23) (1 + ir)N 1 − where N is the lifespan of the project, and ir is the interest rate. The lifespan of the project was assumed to be 25 years with a lending rate of 9%, values similar to those adopted in [55]. This equates the CRF to 0.1018. A report by the International Renewable Energy Agency (IRENA) in 2014 [56] puts the total O&M of an entire CSP plant between 0.02 and 0.04 $/kWh. For the purpose of this paper, because the work was limited only to the heliostat field and thermal power, the lower end of the spectrum (0.02 $/kWht), was taken as the O&M cost. The annual thermal energy at the receiver’s aperture, Eth is given by the summation of the product of the instantaneous optical efficiency value for each heliostat, heliostat area, and the instantaneous beam radiation befalling an individual heliostat for all heliostats in the field (this also represents the power sent out from each individual heliostat). The power from each heliostat is then summed over the beam radiation at all sunshine hours on a representative day of the month [31], I_day. This is done for all months in the calendar year. Equation (24) describes the annual thermal energy at the receiver surface:   XHel  YearX    Eth =  ηhel I Ah (24)  × ×  1 I_day where Ah is the heliostat area, ηhel is the instantaneous heliostat optical efficiency, I is the instantaneous beam radiation during sunshine hours, and Hel is the number of heliostats in the field. Only some days in the year are recommended to be used as average days for the month, and those were used in this work. The total heliostat field cost is a function of the tower cost, receiver cost, and heliostat cost. The cost model utilized in the National Renewable Energy Laboratory’s (NREL) System Advisor Model (SAM) is applied here [57–59]. The system cost in SAM is limited only to direct capital costs. As an example, the computed value for the LCOH in the Gemasolar plant (using Equation (22) with heliostat field cost at $114,260,000 and Eth at 408.330 GWht, as depicted in [55]) is 0.0485 $/kWht. This result assumes a CRF value of 0.1018 and O&M at 0.02 $/KWht. The optimization code was developed using GA [37,60,61]. This algorithm uses the design variables (Table2) to calculate the objective function. The algorithm picks the design variables randomly and uses them as parents to produce the children for the next generation in achieving the optimal solution. In order to reduce computational expense, lower and upper bounds for the design variables are set during optimization. The variables are initially made to assume the values of the Gemasolar plant.

Table 2. Conventional Field Model design variables with lower and upper bounds.

Design Variables Variables Range Number of Heliostats in 1st row (Zone 1) 10–46 Heliostat Area (m2) 25–120 Receiver Dimensions (m2) 25–226 Tower Height (m) 25–140 Heliostat Row Separation Distance Zone 1 (m) (0.866 1.666) DM − × Heliostat Separation Distance Zone 2 (m) (0.866 2.666) DM − × Heliostat Separation Distance Zone 3 (m) (0.866 3.666) DM − ×

One of the defining constraints in the optimizer is the thermal power of the field. With a random selection of design variables, it is possible to reach a value that is below or above the set goal of 50 Sustainability 2020, 12, 2402 12 of 22

MWth. The optimizer is then made to disregard such results from the population. The results of the conventional field from the optimization in the model developed are summarized in Table3.

Table 3. Summary of key results from the 50 MWth Conventional Power Tower field from the model developed and System Advisor Model (SAM).

Parameter Model System Advisor Model (SAM) Heliostat Area (m2) 95.17 95.17 Central Tower Height (m) 91.48 83.98 Central Receiver Area (m2) 55.84 91.43 Levelized Cost of Heat, LCOH ($/kWht) 0.0474 0.0481 Power (MWth) 49.89 50 Efficiency Design Point (%) 60.01 - Mean Annual Efficiency (%) 54.80 55.63 Reflective Surface Area (m2) 152,270.72 136,011.51 Annual Energy (MWht) 150,768.00 149,560.720 System Cost ($) 40,652,834.350 41,253,240.000

An appropriate design point at the identified site (Latitude: 12.39◦ N Longitude: 7.60◦ E) is selected during the summer solstices, signifying a high sun position. It should, however, be noted that the DNI frequency distribution (in the form of a diagram) shows the date for high sun position at the identified site is not the usual summer solstice date of June 21st for locations north of the equator, but instead on April 20th. A DNI design point power of 640 W/m2 was chosen. The value representsSustainability a safe threshold2020, 12, 2402 of thermal rating, which the receiver will not exceed, thereby14 of 24 ensuring appropriate sizing. For arepresents 50 MWth a safe field, threshold the LCOH of thermal obtained rating, which was 0.0474 the receiver $/kWh, will not with exceed, the thereby annual ensuring thermal energy at 150,768.00appropriate MWth, sizing. and the total field cost at $40,652,834.350. The mean annual efficiency for the designed andFor optimized a 50MWth plant field,was the LCOH 54.80%. obtained In order was 0.0474 to further $/kWh, validate with the annual the model thermal developed, energy SAM at 150,768.00 MWth, and the total field cost at $40,652,834.350. The mean annual efficiency for the was used todesigned generate and and optimized optimize plant awas 50 54.80%. MWth In field. order The to further results validate were the then model compared developed, with SAM the model developed.was To used calculate to generate the and LCOH optimize using a 50MWth SAM, field. Equation The results (22) were was then applied compared using with the the same model values for the CRF. Thedeveloped. comparison To calculate between the LCOH the using results SAM, isEquation shown again(22) was in applied Table using3. A the marginal same values di ff forerence was observed inthe the CRF. LCOH The comparison from both between models, the results showing is shown a good again correlation. in Table3. A marginal di fference was observed in the LCOH from both models, showing a good correlation. In Figure7In, Figurethe field7, the layout field layout from from the the conventional conventional field field model model is shown, is shown, representing representing the mean the mean annual heliostatannual heliostat efficiency. efficiency.

Figure 7.FigureField 7. layoutField layout of a of 50 a 50MWth MWth Conventional Power Power Tower Tower System. System.

3.2. Multi-Tower Field In the multi-tower field, one of the first questions to address is the position in which the auxiliary tower will be placed. The auxiliary tower location was calculated based on the region with the lowest efficiency and reflected energy. The average annual heliostat efficiency representation of the field was evaluated to aid in identifying the region with the lowest efficiency. In order to simplify the computation, the field was divided only into four quadrants when computing the position of the auxiliary tower as shown in Figure8. The results are tabulated in Table4. Sustainability 2017, 9, x FOR PEER REVIEW 12 of 22

Mean Annual Efficiency (%) 54.80 55.63 Reflective Surface Area (m2) 152,270.72 136,011.51 Annual Energy (MWht) 150,768.00 149,560.720 System Cost ($) 40,652,834.350 41,253,240.000

For a 50MWth field, the LCOH obtained was 0.0474 $/kWh, with the annual thermal energy at 150,768.00 MWth, and the total field cost at $40,652,834.350. The mean annual efficiency for the designed and optimized plant was 54.80%. In order to further validate the model developed, SAM was used to generate and optimize a 50MWth field. The results were then compared with the model developed. To calculate the LCOH using SAM, Equation 22 was applied using the same values for the CRF. The comparison between the results is shown again in Table 3. A marginal difference was observed in the LCOH from both models, showing a good correlation. In Figure 7, the field layout from the conventional field model is shown, representing the mean annual heliostat efficiency.

N

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Sustainability 2020, 12, 2402 13 of 22 Figure 7. Field layout of a 50MWth Conventional Power Tower System.

3.2.3.2. Multi-Tower Multi-Tower Field Field InIn the the multi-tower multi-tower field, field, one one of of the the first first questions questions to to address address is is the the position position in in which which the the auxiliary auxiliary towertower will will be be placed. placed. The The auxiliary auxiliary tower tower location location was was calculated calculated based based on on the the region region with with the the lowest lowest effiefficiencyciency and and reflected reflected energy. energy. The The average average annual annual heliostat heliostat e ffiefficiencyciency representation representation of of the the field field waswas evaluated evaluated to to aid aid in in identifying identifying the the region region with with the the lowest lowest e ffiefficiency.ciency. In In order order to to simplify simplify the the computation,computation, the the field field was was divided divided only only into into four four quadrants quadrants when when computing computing the the position position of of the the auxiliaryauxiliary tower tower as as shown shown in in Figure Figure8. 8. The The results results are are tabulated tabulated in in Table Table4. 4.

(a) (b)

FigureFigure 8. 8.(a )(a Position) Position of theof the four four identified identifi quadrantsed quadrants in the in field. the field. (b) Description (b) Description of the regionof the inregion which in thewhich additional the additional tower would tower be would sighted. be sighted.

TableTable 4. 4Mean Mean annual annual e ffiefficiencyciency at at the the four four identified identified quadrants. quadrants. Averaged Annual Averaged Annual Averaged Annual Averaged Annual Efficiency in the 1st Efficiency in the 2nd Efficiency in the 3rd Efficiency in the 4th Quadrant (%) Quadrant (%) Quadrant (%) Quadrant (%) 57.14 56.24 54.37 53.37

The results in Table4 clearly show the region with the least mean annual e fficiency value. This is predominantly a result of the more substantial cosine losses in that region of the field. This corroborates evidence that plant locations north of the equator favour north-facing fields [36,38]. The additional tower to be introduced into the field is hence sited at the central position of the weakest quadrant, the 4th quadrant (see Figure8b). With the multi-tower field now generated, the criteria for how the heliostats aim at the receivers in the field were defined. The heliostats are not restricted in terms of which tower they are allowed to focus on. Each heliostat makes a decision about the receiver to aim at based on the strength of the reflected radiation. In other words, optical efficiency losses are computed for each heliostat in the two scenarios: aiming at the central tower and aiming at the auxiliary tower. The aim point bearing the lesser loss, for all the combined optical efficiency loss parameters, is selected. An overall assessment of the potential of adding an auxiliary tower to the 50 MWth optimized conventional field was conducted. This assessment can be considered as an evaluation for upgrading or retrofitting a pre-existing conventional field. The auxiliary tower was added under varying receiver dimensions, tower height and tower displacement distance. Variables’ ranges for the auxiliary tower are highlighted in Table5. The results in Figure9a,b show an evident increase in the field e fficiency values and the thermal energy for different combinations of additional tower input variables (Table5). In Figure9a, at no point does the LCOH of the field with the auxiliary tower and converge with the conventional field, signifying that at that particular field power, the auxiliary tower would always have a higher LCOH. With increasing values of the design variables, the LCOH of the auxiliary tower becomes higher (Figure9a). Sustainability 2017, 9, x FOR PEER REVIEW 13 of 22

Averaged Annual Averaged Annual Averaged Annual Averaged Annual Efficiency in the 1st Efficiency in the 2nd Efficiency in the 3rd Efficiency in the 4th Quadrant (%) Quadrant (%) Quadrant (%) Quadrant (%) 57.14 56.24 54.37 53.37

The results in Table 4 clearly show the region with the least mean annual efficiency value. This is predominantly a result of the more substantial cosine losses in that region of the field. This corroborates evidence that plant locations north of the equator favour north-facing fields [36,38]. The additional tower to be introduced into the field is hence sited at the central position of the weakest quadrant, the 4th quadrant (see Figure 8b). SustainabilityWith the2020 multi-tower, 12, 2402 field now generated, the criteria for how the heliostats aim at the receivers14 of 22 in the field were defined. The heliostats are not restricted in terms of which tower they are allowed to focusTable on. 5.EachMulti-tower heliostat (one makes additional a decision tower) about field model the receiver design variables to aim at with based lower on and the upper strength bounds. of the reflected radiation. In other words, optical efficiency losses are computed for each heliostat in the two scenarios: aiming at theDesign central Variables tower and aiming at the auxiliary tower. Variables The Rangeaim point bearing the lesser loss, forNumber all the ofcombined Heliostats optical in 1st row efficiency (Zone 1) loss parameters, is selected. 10–46 An overall assessmentHeliostat of the Area potential (m2) of adding an auxiliary tower 25–120to the 50MWth optimized conventional field was conducted. This assessment can be considered as an evaluation for upgrading Receiver Dimensions (m2) 25–226 or retrofitting a pre-existing conventional field. The auxiliary tower was added under varying Tower Height (m) 25–140 receiver dimensions, tower height and tower displacement distance. Variables’ ranges for the Heliostat Row Separation Distance Zone 1 (m) (0.866–1.666) DM auxiliary tower are highlighted in Table 5. The results in Figures 9a and 9b show× an evident increase in the field efficiencyHeliostat Separationvalues and Distance the thermal Zone 2 ener (m)gy for different combinations (0.866–2.666) ofDM additional tower × input variablesHeliostat (TableSeparation 5). In Figure Distance 9a, at Zoneno point 3 (m) does the LCOH of the (0.866–3.666) field with theDM auxiliary tower × and convergeAdditional with the Towerconventional Placement field, Distance signifying (m) that at that particular ((0.866–1.666) field DM)power,+ Df the auxiliary tower would always have a higher LCOH. With increasing values of the design× variables, the LCOH Additional Tower Height (m) 25–140 of the auxiliary tower becomes higher (Figure 9a). Additional Tower Receiver Dimensions (m2) 25–226

0.5 58 Conventional Field 0.4 One Additional MultiTower Field 56

0.3 Conventional Field One Additional MultiTower Field 54 0.2 52 0.1

0 50 0 200 400 600 800 1000 1200 1400 1600 0 200 400 600 800 1000 1200 1400 1600 Run Number Run Number 105 0.62 1.8 Conventional Field Conventional Field One Additional MultiTower Field One Additional MultiTower Field 0.6 1.7

0.58 1.6

0.56 1.5 0 200 400 600 800 1000 1200 1400 1600 0 200 400 600 800 1000 1200 1400 1600 Run Number Run Number

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FigureFigure 2 a) 9. Levelized(a) Levelized Cost Costof Heat of (LCOH) Heat (LCOH) and energy and energyoutput outputwith one with addition one additionalal multi-tower multi-tower system b)system thermal (b power) thermal and power mean andannual mean efficiency annual ewithfficiency one additional with one additional multi-tower multi-tower system. system.

TheThe additional additional designdesign variables variables for thefor multi-towerthe multi-tower configuration configuration were utilized were inutilized the optimization in the optimizationprocess for theprocess 50 MWth for the field 50MWth with the field same with objective the same function objective of function LCOH highlighted of LCOH highlighted earlier. This earlier.increased This the increased number the of number design variables of design used variab inles the used optimization in the optimization process. The process. updated The number updated of numberdesign of variables design isvariables highlighted is highlighted in Table5. in Table 5. Here, Df is the final distance between the central tower and the furthest heliostat in the same-axis directionTable of5 Multi-tower the auxiliary (one tower. additional tower) field model design variables with lower and upper bounds.In the multi-tower setup, the same objective function as the conventional field was used: minimizing the LCOH. However, in order to simplify the solution process, additional objectives Design Variables Variables Range were added and handledNumber as of constraints. Heliostats in These1st row include (Zone 1) the total heliostat 10–46 reflective surface area and the field efficiency. This is in addition to the initial constraint limiting the optimizer to computing results only at a field power of 50 MWth. For the field efficiency, only values that are higher than the computed result from the conventional setup are considered in the optimizer. The total reflective surface area, on the other hand, limits the optimizer from finding solutions that exceed the total reflective surface area of the conventional field. After a certain number of repeated optimizations runs, the minimal value of LCOH was recorded, after achieving a low spread between the lowest and highest value of the objective function [62]. Sustainability 2020, 12, 2402 15 of 22

4. Results and Discussion The results from the optimization process are highlighted in Table6. In order to provide a comparative description, the results from the multi-tower field are compared to the results from an optimized single-tower conventional field. The results are all tabulated in Table6.

Table 6. Results: Conventional field, and multi-tower field.

Conventional Multi-Tower Field Parameter Field (One Additional Tower) Heliostat Area (m2) 95.17 93.99 Central Tower Height (m) 91.48 92.91 Central Receiver Area (m2) 55.84 40.36 Auxiliary Tower Height (m) - 92.94 Auxiliary Receiver Area (m2) - 66.38 LCOH ($/kWht) 0.0474 0.0579 Field Power (MWth) 49.89 49.79 Efficiency Design Point (%) 60.01 62.95 Mean Annual Efficiency (%) 54.80 58.44 Mean Annual Attenuation Efficiency (%) 96.52 97.07 Mean Annual Shadowing and Blocking Efficiency (%) 95.96 96.84 Mean Annual Cosine Efficiency (%) 77.84 84.47 Mean Annual Interception Efficiency (%) 87.82 92.70 Reflective Surface Area (m2) 152,270.72 140,987.00 Number of Heliostats 1600 1500 Annual Energy (MWht) 150,768.00 153,788.27 Auxiliary Receiver Thermal Power (MWth) - 11.51 System Cost ($) 40,652,834.35 57,198,009.00

As shown in Table6, the additional tower for the multi-tower field results in a marked increase in the optical field efficiency value. A 3.64% increase in the mean annual field efficiency and a 2.94% increase in the design point efficiency is observed when compared to the results obtained in a conventional field setup. The most considerable improvement in optical efficiency is seen in the cosine efficiency value. This is primarily because the additional tower in the field provides an alternate aim point for the heliostats with the least reflecting efficiency. The LCOH, however, is higher in the new configuration. This indicates that the benefits due to the increment in the optical efficiency values and annual energy output do not outweigh the cost of installing an additional tower and receiver. In the new configuration, the number of heliostats aiming at the one auxiliary tower changes through the months and through the day (see Figure 10). At the design point date, April 20th, a total number of 317 heliostats aim at the auxiliary tower at solar noon (Figure 10a). The number of heliostats aiming at the auxiliary tower at solar noon peaks in January and December, when the sun’s position is low, making it difficult for the ‘weak’ heliostats to reflect radiation onto the main central tower without incurring enormous cosine losses (Figure 10a). On the other hand, during sunshine hours, and at around solar noon, a reduced number of heliostats aim at the auxiliary tower (Figure 10b). This is predominately due to the lesser cosine losses from the heliostats aiming at the main central tower, hence the central tower becomes a preferred target. The computed thermal power rating of the auxiliary tower was 11.51 MWth. The main central tower, which caters to the bulk of the heliostats in the field, now has a computed thermal rating of 38.28 MWth. In Figure 11a,b, the month-on-month variation of the total energy output and mean efficiency values for both the conventional field and the multi-tower field is shown. A marked improvement in the mean efficiency value was observed from January to December in the two models shown in Sustainability 2017, 9, x FOR PEER REVIEW 15 of 22

The LCOH, however, is higher in the new configuration. This indicates that the benefits due to the increment in the optical efficiency values and annual energy output do not outweigh the cost of installing an additional tower and receiver. In the new configuration, the number of heliostats aiming at the one auxiliary tower changes through the months and through the day (see Figure 10). At the design point date, April 20th, a total number of 317 heliostats aim at the auxiliary tower at solar noon (Figure 10a). The number of heliostats aiming at the auxiliary tower at solar noon peaks in January and December, when the sun’s position is low, making it difficult for the ‘weak’ heliostats to reflect radiation onto the main central tower without incurring enormous cosine losses (Figure 10a). On the other hand, during sunshine hours, and at around solar noon, a reduced number of heliostats aim at the auxiliary tower (Figure 10b). This is predominately due to the lesser cosine losses from the heliostats aiming at the main centralSustainability tower,2020 hence, 12, 2402the central tower becomes a preferred target. 16 of 22 The computed thermal power rating of the auxiliary tower was 11.51 MWth. The main central tower, which caters to the bulk of the heliostats in the field, now has a computed thermal rating of Figure 11b. In Figure 11a, it is worth mentioning that the dip witnessed during months 6–8 is a result 38.28 MWth. of the poor DNI values, as a result of cloud cover during that period (from NiMet data).

Heliostats Aiming at Auxiliary Tower Heliostats Aiming at Auxiliary Tower, (Jan-Dec) Design Point (April 20th) 450 450 400 400 350 350 300 300 250 250 200

200 Heliostats 150

Heliostats 150 100 100 50 50 0 0 6 7 8 9 10 11 12 13 14 15 16 17 18 123456789101112 Time (hrs) Month One Auxiliary Tower One Auxiliary Tower

(a) (b)

FigureFigure 3 a) 10. Heliostats(a) Heliostats aiming aiming at the at theauxiliary auxiliary tower tower through through the theyear; year; b) (Heliostatsb) Heliostats aiming aiming at the at the Sustainability 2017, 9, x FOR PEER REVIEW 16 of 22 auxiliaryauxiliary tower tower during during sunshine sunshine hours hours at the at the design design point point date. date.

Total Monthly Mean Efficiency Output In Figures 11a and 11b, the month-on-month variation0.6 of the total energy output and mean efficiency values for both the conventional field and the multi-tower fieldOne is Auxiliary shown. Tower Field A marked Conventional Field improvement in the mean efficiency value was observed from0.59 January to December in the two models shown in Figure 11b. In Figure 11a, it is worth mentioning that the dip witnessed during months 6– 0.58 8 is a result of the poor DNI values, as a result of cloud cover during that period (from NiMet data).

0.57

0.56 Monthly Energy Output (kWht) Energy Monthly 0.55

0.54 024681012 Month (a) (b)

FigureFigure 4 11.a) Total(a) Total monthly monthly energy energy output, output, conventional conventional and and one one additional additional tower tower field; field; b) (b Total) Total monthlymonthly mean mean efficiency efficiency output, output, conventi conventionalonal and and one one additional additional tower tower field. field.

AA more more explicit explicit demonstration demonstration of of the the effect effect of of the the multi-tower multi-tower field field is is shown shown in in Figure Figure 12. 12 The. The meanmean annual annual efficiency efficiency field field layout layout for for the the conventi conventionalonal system system and and the the one one additional additional tower tower field field is is seenseen in in Figure Figure 12a12a,b. and The 12b. change The change in shading in shadin matricesg matrices of the optical of the losses optical model losses from model the conventional from the conventionalfield to the multi-tower field to the multi-tower field is shown field in Figureis shown 12 c–i.in Figure 12c–i. The entire optimization for the multi-tower field was initially made for a 50 MWth field. A broader range of thermal power was examined, so a more critical analysis of the effect of a multi-tower field

can be observed. Figure 13 showsN the LCOH results from both the conventional field modelN and the multi-tower field model at various-powerW E thermal field values. W E S S

(a) (b)

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(c) (d) Sustainability 2017, 9, x FOR PEER REVIEW 16 of 22

seen in Figure 12a and 12b. The change in shading matrices of the optical losses model from the conventional field to the multi-tower field is shown in Figure 12c–i.

Sustainability 2020, 12, 2402 17 of 22

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Sustainability 2017, 9, x FOR PEER REVIEW 17 of 22 (c) (d)

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Figure 12. a, c, g, i) Conventional field: mean annual efficiency, cosine, attenuation, shadowing & blocking and interception efficiency respectively. b, d, f, h, j) Multi-tower field, one additional tower: mean annual efficiency, cosine, attenuation, shadowing and blocking and interception efficiency respectively.

The entire optimization for the multi-tower field was initially made for a 50MWth field. A broader range of thermal power was examined, so a more critical analysis of the effect of a multi- tower field can be observed. Figure 13 shows the LCOH results from both the conventional field model and the multi-tower field model at various-power thermal field values. Sustainability 2017, 9, x FOR PEER REVIEW 17 of 22

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FigureFigure 12. 12. a, (c,a, cg,,g ,i)i) Conventional Conventional field: field: mean mean annual annual effi efficiency,ciency, cosine, cosine, attenuation, attenuation, shadowing shadowing & blocking& blocking and andinterception interception efficiency efficiency respectively. respectively. b, d, f, (h,b, dj), fMulti-tower,h,j) Multi-tower field, one field, additional one additional tower: meantower: annual mean efficiency, annual e fficosine,ciency, attenuation, cosine, attenuation, shadowing shadowing and blocki andng and blocking interception and interception efficiency Sustainabilityrespectively.efficiency 2017 respectively., 9 , x FOR PEER REVIEW 18 of 22

The entire optimization0.0700 for the multi-tower field was initially made for a 50MWth field. A broader range of thermal power was examined, so a more critical analysis of the effect of a multi- 0.0650 tower field can be observed. Figure 13 shows the LCOH results from both the conventional field model and the multi-tower0.0600 field model at various-power thermal field values. 0.0550

0.0500

LCOH($/KWht) 0.0450

0.0400

0.0350 0.00 100.00 200.00 300.00 400.00 500.00 600.00 700.00 Power (MWth)

LCOH Conventional ($/KWht) One Additional Tower ($/KWht)

FigureFigure 13. 13. LevelizedLevelized Cost Cost of of Heat Heat (LCOH) (LCOH) for for a a conv conventionalentional field field and a multi-tower field. field.

Results from Figure 13 clearly show the promising LCOH trend of multi-tower fields fields at higher thermalthermal power power figures figures and larger fields. fields. In In larger larger fields, fields, a a higher number of of weaker heliostats are are witnessed in the field, field, making the need for and use of an additional tower all the more critical. The heliostats at the weaker weaker region region of a a multi-tower multi-tower field field are are provided provided with an additional additional tower tower to to reflect reflect thethe sun’ssun’s radiation,radiation, thereby thereby considerably considerably cutting cutting down down on cosine,on cosine, spillage spillage and attenuationand attenuation losses whichlosses whichin turn in gives turn rise gives to higher rise to total higher energy total output. energy At output. a certain At point,a certain as seen point, in theas seen trend, in the the multi-tower trend, the multi-towerfield continuously field continuously provides a lower provides LCOH a valuelower comparedLCOH value to a compared conventional to a field conventional of similar thermalfield of similarpower. Thisthermal is seen power. explicitly This atis theseen 400 explicitly MWth range at the in 400MWth the one auxiliary range in tower the configuration,one auxiliary wheretower configuration,expanding the where conventional expanding field the in orderconventional to attain field a higher in order thermal to attain field a output higher becomes thermal lessfield e ffoutputective becomesdue to the less significant effective opticaldue to lossesthe significant gained as optical a result losses of the gained size of as the a result field. of the size of the field.

5. Conclusions Conclusions InIn power towertower systems,systems, the the heliostat heliostat field field is is one one of of the the essential essential subsystems, subsystems, comprising comprising 40%–50% 40%– 50%of the of plant’s the plant’s total total investment investment cost andcost ofand about of abou 40%t 40% of the of plant’s the plant’s overall overall power power losses. losses. Different Different field field configurations are therefore being investigated. Multi-tower systems provide an alternative approach in which the heliostat field efficiencies can be increased. In this paper, a different architecture of the multi-tower configuration is investigated. The configuration explored, which provides a different take to the usual mainstream multi-tower configuration, involves adding an auxiliary tower to an existing surrounding conventional field. As a case study, the multi-tower configuration was applied in Katsina, Nigeria, and the field parameters were optimized for 50MWth field power. To identify the position in which the auxiliary tower was sighted, the mean annual field efficiency of the 50MWth conventional field was computed. The results clearly showed that the southern region, which had heliostats with huge cosine losses, had the least mean annual efficiency value of heliostats. The presence of the auxiliary tower provided an overall increase in the system efficiency of the field by reducing some of the losses entailed in a conventional single-tower setup, by providing the ‘weaker’ heliostats in the region a more favourable tower to target. A reduction in attenuation, spillage and cosine losses by 0.55%, 4.88% and 6.63%, respectively, was observed in the multi-tower configuration. This led to an overall increase in the mean annual efficiency of the field by 3.64%. With most heliostats on the multi-tower configuration targeting the main central tower in the 50MWth field, the auxiliary tower’s contribution to the LCOH becomes limited. This can be seen in the small increment of 3,020MWht recorded in the thermal field energy output. The LCOH is thus higher in the new configuration. This indicated that the size of the field limits the potential contribution of the auxiliary tower at 50MWth. Similarly, the benefits due to the increment in the Sustainability 2020, 12, 2402 19 of 22 configurations are therefore being investigated. Multi-tower systems provide an alternative approach in which the heliostat field efficiencies can be increased. In this paper, a different architecture of the multi-tower configuration is investigated. The configuration explored, which provides a different take to the usual mainstream multi-tower configuration, involves adding an auxiliary tower to an existing surrounding conventional field. As a case study, the multi-tower configuration was applied in Katsina, Nigeria, and the field parameters were optimized for 50 MWth field power. To identify the position in which the auxiliary tower was sighted, the mean annual field efficiency of the 50 MWth conventional field was computed. The results clearly showed that the southern region, which had heliostats with huge cosine losses, had the least mean annual efficiency value of heliostats. The presence of the auxiliary tower provided an overall increase in the system efficiency of the field by reducing some of the losses entailed in a conventional single-tower setup, by providing the ‘weaker’ heliostats in the region a more favourable tower to target. A reduction in attenuation, spillage and cosine losses by 0.55%, 4.88% and 6.63%, respectively, was observed in the multi-tower configuration. This led to an overall increase in the mean annual efficiency of the field by 3.64%. With most heliostats on the multi-tower configuration targeting the main central tower in the 50 MWth field, the auxiliary tower’s contribution to the LCOH becomes limited. This can be seen in the small increment of 3020MWht recorded in the thermal field energy output. The LCOH is thus higher in the new configuration. This indicated that the size of the field limits the potential contribution of the auxiliary tower at 50 MWth. Similarly, the benefits due to the increment in the optical efficiency values and annual energy output do not out-weigh the cost of installing an additional tower and receiver. In larger fields, a more significant number of weak heliostats are witnessed. The poorly reflecting heliostats are provided with an additional tower to reflect the solar radiation to, thereby considerably cutting down on some optical losses, which in turn gives rise to higher energy output. A continuous reduction in the LCOH for larger fields is seen as a result. At a thermal field power rating of 400 MWth, the multi-tower configuration provides a higher LCOH compared to a conventional field with similar power. The growth and development of power tower systems has seen larger systems, up to 150MWe, being built around the world. The multi-tower configuration provides a viable alternative way in which such large power tower systems can be built, by potentially providing a lower LCOH and higher plant efficiency. The configuration could also be applied in existing fields by updating or retrofitting existing conventional fields and adding auxiliary towers. The study here provides a quick overview of auxiliary towers in a multi-tower field configuration. In further studies, the effect of the field configuration on the whole plant, especially on the storage subsystem, can be investigated. Furthermore, techniques for developing the field by reconfiguring the field layout to reflect the multi-towered setup can also be studied in future work.

Author Contributions: P.K., C.S. and Z.A.H. are responsible for the conceptualization, methodology, formal analysis, and investigation of the project. Z.A.H. is responsible for model development, writing the original article draft and data visualization. P.K. is responsible for technical support, model analysis and validation. P.K. and C.S. are responsible for the project administration, funding acquisition, resources, and reviewing and editing the article. All authors have read and agreed to the published version of the manuscript. Funding: The research was funded by the Petroleum Technology Development Fund (PTDF) in Nigeria as part of oversees scholarship scheme on research. Conflicts of Interest: The authors declare no conflict of interest.

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